Question

When two vectors are normal, the magnitude of their resultant is root10. When the
same vectors are inclined at 60°, their resultant is root13

The magnitudes of vectors are​

Answer 1

Given that magnitude of resultant is √15 of they are right angled.And magnitude of resultant is √18 if they are at 60° to each other.

We know that

The magnitude of resultant force is A which equals

A=√(a^2+b^2+2abcosα) where α is angle between two forces.

From the above information we can write as

a^2+b^2=15 and

a^2+b^2+2abcos60°=18 substitute above result in this one we get,

ab=3,

By knowing, a^2+b^2 and an values we can obtain

The value of a+b and a-b as follows,

(a +b) =√(a^2+b^2+2ab)=√21, and

(a-b) =√(a^2+b^2–2ab)=√9=3.

Solving above two equations we get,

a=( √21 + 3)/2 and

b=(√21 - 3)/2.

Answer 2

Answer:

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